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- anonymous

will give medal and fan!

- schrodinger

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- anonymous

The function H(t) = -16t2 + vt + s shows the height H (t), in feet, of a projectile launched vertically from s feet above the ground after t seconds. The initial speed of the projectile is v feet per second.
Part A: The projectile was launched from a height of 100 feet with an initial velocity of 60 feet per second. Create an equation to find the time taken by the projectile to fall on the ground. (2 points)
Part B: What is the maximum height that the projectile will reach? Show your work. (2 points)
Part C: Another object moves in the air along the path of g(t) = 20 + 38.7t where g(t) is the height, in feet, of the object from the ground at time t seconds.
Use a table to find the approximate solution to the equation H(t) = g(t), and explain what the solution represents in the context of the problem? [Use the function H(t) obtained in Part A, and estimate using integer values] (4 points)
Part D: Do H(t) and g(t) intersect when the projectile is going up or down, and how do you know? (2 points)

- JoannaBlackwelder

We are given the function with constants for the height and speed. Can you plug them in?

- anonymous

H(t)=-16t^2+100(60)+s would that right @JoannaBlackwelder

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- anonymous

- anonymous

- JoannaBlackwelder

Close, I get: 16t^2 + 60t +100

- JoannaBlackwelder

v=60
s=100

- anonymous

can you help me with parts c and d @JoannaBlackwelder

- JoannaBlackwelder

Sure, can you make a table of values of H(t) and g(t)?

- anonymous

g(t) h(t)
1 58.7 144
2 97.4 156
3 136.1 136
4 174.8 84

- anonymous

is that ok @JoannaBlackwelder

- JoannaBlackwelder

Yep, that's a good start? Do you know what we are looking for in the table?

- anonymous

the point were h(t)=g(t)

- JoannaBlackwelder

Yep, the point or points. :-) Do you see one so far?

- anonymous

at 3 they are the closest

- JoannaBlackwelder

Yep, I think we can say they are about the same at t=3. :-) So, what does that represent in the problem?

- anonymous

the point were they intersect?

- JoannaBlackwelder

Yep, that would be the point where the two objects would hit each other. :-)

- anonymous

for part d how do I know whether or not it is going down or up?

- JoannaBlackwelder

It would be going up if it is before the vertex, down if it is after.

- JoannaBlackwelder

Since the parabola is upside down

- anonymous

it would be going down ,right?

- JoannaBlackwelder

Yep :-)

- anonymous

can you help me with a couple more equations.

- JoannaBlackwelder

Possibly. But open a new question, please. And tag me :-)

- anonymous

ok

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